from the ship point of view, the ship's going out, it's gonna see five flashes, 12 minutes apart, that's gonna be 60 minutes, okay? now, coming back in, the ship's gonna see flashes, how many minutes apart? oh, you don't remember that. three, okay? so, the ship is gonna see those flashes three minutes apart, okay? how many flashes is the ship gonna get in its one hour, three minutes apart? you've gotta figure out how many 3's will go into 60? - 20. - 20. so, the ship is gonna see 20 flashes coming back in, yeah? more flashes coming back in than going out. i mean when the rain's coming down like this, you get fewer drops hitting you per minute, this way. but when you turn around and ba-ba-ba-ba-bam, okay, same type thing here. now, we get 20 flashes coming in, 3 minutes apart, twenty 3s is 60. okay? so what time is it on the ship?

120 minutes. two hours. what time is it on the earth? how many flashes have been emitted on the earth during this trip? 25! so, from the earth... 25 x 6 is what, gang? mmm! eee! now, let me ask you a question. you know, when you see these guys, they got the green pea and they got the three jars and they go like this, like that, all right. which one's it under? and you always guess wrong. but you know, there's a catch, because they're pulling-- they're very, very skilled, and they're pulling something over on you, right? and you always-- or a card trick, right? dah-dah-dah-dah-dah, right? where's the catch?

i've got a friend that does the card tricks. how do you even suspect? this guy is so good i've even suspected him of really being magic and pretending he has skill. you know what i mean? he's so good, okay. but anyway, there's always a trick. where's the trick here, gang? where did i trick you into thinking that 2 hours on one frame of reference would be seen 2 1/2 hours on-- does that make sense? what did einstein say common sense was? that layer of prejudices laid down usually by the age of 18. this does not make sense to you, because you know why? it's not part of your background. it's not part of your experience. this is off your experience. maybe jet planes wouldn't make sense to a caveman and this stuff is just starting to make sense to us, yeah. i'll tell you what, gang? there's no catch, as we understand it, nature is this way. many, many experiments to see if there's something wrong about this and all these experiments have only gone into confirming that einstein was right.

let me say a neat thing about science too. in a lot of fields, there'll be some sort of hero like einstein's our hero, here. we all love einstein. most of us do, yeah. so, einstein's our hero, and you tend to think, "well, if he's a hero, you don't wanna take shots at him." but in science, it's different. in science, say "hero-schmero." everybody is trying to crack that hero and find something wrong. everyone's attacking to see if they can find something wrong. and so science doesn't rest upon the reputation of some hero. science rests upon everyone else trying to find a crack in that theory. and all attempts, so far, have only gone on to substantiate this: time really is different when you're moving. but i'll tell you what? we're gonna talk more about these ideas next time and you know what i wanna do for you now? i wanna share with you a film that a friend of mine made way back in 1976. when i was teaching these ideas in the early '70s, i discovered this kind of treatment at the class board. that's one thing about teaching, you learn at the class board.

you know, you guys aren't the only one's learning. i learn too. and what i did at that time was to be able to see the ship at different positions. i made a whole lot of drawings, cartoons, and i took photographs and made slides. and i would get at the back of the room and i'd show this slides in quick succession. i'd have a carousel, i'd hold the things, i'll go click, click, click, click, show the slides, so you guys could see the ship at different positions. and about that time, my first edition of the book was out and i went to a party over in berkeley and there was a fellow there who had just graduated from san francisco state, who was showing some of his movies. he was into moviemaking, cartoons. i really liked his cartoons. they had a warmth to them. i really liked him: steve smith. i said, "steve, you know, i've got this little thing i do "with these little slides. "i wonder maybe you could make up a little cartoon movie. we could make a movie of this and share it with more people." and at that time, he was working as a dishwasher down on telegraph avenue. and i said, "steve, quit the dishwashing. "i'll grubstake you. i'll get you groceries. "i'll feed you and i'll grubstake me. "maybe city college will let you use some of their equipment

and we'll make a little animated movie." and he made an animated movie on everything that we-- would you like to see it? okay. roll it, lionel. we'll see it right here, gang. right here. ♪ where did the time go? ♪ does anybody, does anybody know? ♪ ♪ when did the day break? ♪ did someone drop it, was it a mistake? ♪ ♪ la, la, la, la la, la, la... did you know that time's different when you move at different speeds, that when you move through space, you change the rate at which you move into the future?

well, you can't really notice these differences for everyday speeds, but for really high speeds like for rockets traveling about half the speed of light, these time differences can be noticed. let's take a look at the so-called twin paradox. well, bye. i don't know if i'll see you again. and while the traveling twin experiences weeks... the stay-at-home twin experiences years.

you know, i think i'll just sit here and do nothing. that sounds like-- yeah, i'll do that. now, what? what? what is going on out there? ah, my goodness... hey. i don't believe this. look at you. - good to see you. - i must relax. i can't relax. i'm too old to relax. look at the size of this one, will you? could a situation like this be true? you bet it can. this is time dilation. we can see time dilation by comparing clocks from different frames of reference. say, from the earth and from a high-speed rocket ship. now, a clock can be anything that measures periodic intervals of time. to simplify, we're gonna let the ticks of our clock be periodic flashes of light. look at the light flashes

emitted by the stationary rocket ship. now, some time goes by before they reach the distant planet. but since there's no relative motion involved, successive flashes get to the planet at regularly-spaced intervals. that's to say, both the sender and the receiver will agree on the time intervals between the flashes. now, there's nothing unusual about this. but suppose the rocket ship moves. look at the doppler effect. an observer sees the flashes at shorter intervals. suppose the ship moves fast enough so an observer sees the flashes at intervals twice as short as the ship sends them. then if the ship moves away, just as fast now, an observer's gonna see intervals twice as long. like if the rocket sends a flash every six minutes, they will be seen every 12 minutes by the observer when the rocket moves away, but every three minutes when the rocket's approaching. now, let's apply this to time dilation. if the ship passes by the earth

and moves away at the same high speed for one hour and quickly turns around and then returns in one hour, rocket ship time, this 2-hour trip is seen by the earth as taking place not in 2 hours, but in 2 1/2 hours. and this is because the ship and the earth have been in completely different realms of time. let's look at this in greater detail. suppose that when the ship goes by the earth, that clocks on earth and on the ship are synchronized to 12:00 noon. then, as the rocket leaves the earth, a flash of light is emitted by the ship every six minutes. that's six minutes rocket time. then the ship emits 10 of the 6-minute flashes while going away from the earth. the 10th flash is gonna be emitted 60 minutes after leaving the earth.

then the ship's clock is gonna read 1:00, just when this 10th flash is emitted. now, suppose this is the moment that the ship turns around. our earth observers don't see the turnaround until they see the 10th flash. now, here it comes. it's gonna take some time for it to get to them. closer, closer, closer... and there it is: 10 flashes, 12 minutes apart. that's 120 minutes. two hours. so that means it's 2:00 now on earth. now, the 10 flashes the ship emits when approaching the earth, they are gonna be seen three minutes apart or all 10 in 30 minutes. the first is three minutes after 2:00, earth time, the next is three minutes later and so on, until the last flash is emitted just as the ship whizzes past the earth.

and that's gonna be 2:30, earth time. so a clock aboard the rocket ship reads 2:00, while a clock on the earth reads 2:30. this checks out. check the figures. now, let's go through this once again. watch carefully and compare the clocks.

we'll get the same results if we switch frames of reference. the earth will send flashes now at six-minute intervals and the rocket ship will observe them, while again, departing and returning on, what for the ship is, a two-hour journey. one hour out and one hour back.

while going away, the ship's gonna see flashes 12 minutes apart. that means it's gonna see a total of five flashes during this hour, going away. see that? now, while returning, the ship sees flashes 3 minutes apart. they're gonna see a total of 20 during the hour of return. for the round trip then, the earth emits a total of 25 flashes at 6-minute interval, that's 150 minutes or 2 1/2 hours.

same results as before. so, from either frame of reference, a person on earth ages more than a person in a high-speed rocket ship. it's not so much a question of who's moving and who isn't, but rather the different space-time experienced.

the person on earth remains in one space-time throughout the experiment whereas the person in the rocket ship is in a completely different realm of time while traversing space going away from the earth and in still another realm of time while traversing space and coming back to the earth. that's two space-times, two space-times separated by the acceleration of the ship and turning around. now that acceleration is interesting in its own right. get to that in general relativity, but we see that the details of that acceleration aren't really essential in this case. the principal significance of that acceleration is that it marks the changing from one space-time to another. now, our twins have been in different space-times and they can meet again at the same place in space, but only at the expense of time. isn't that great? that's time dilation. peace. ♪ where did the time go?

♪ does anybody, does anybody know? ♪ ♪ when did the day break? ♪ did someone drop it, was it a mistake? ♪ ♪ i've got a notion, circular motion ♪ ♪ i'm finding ♪ out in the ocean, out in the ocean of time ♪